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All Journal IAES International Journal of Robotics and Automation (IJRA) CAUCHY: Jurnal Matematika Murni dan Aplikasi Kinetik: Game Technology, Information System, Computer Network, Computing, Electronics, and Control Limits: Journal of Mathematics and Its Applications PengabdianMu: Jurnal Ilmiah Pengabdian kepada Masyarakat Contemporary Mathematics and Applications (ConMathA)
Miswanto
Universitas Airlangga
Agriculture, Biological Sciences & Forestry Automotive Engineering Computer Science & IT Control & Systems Engineering Economics, Econometrics & Finance Electrical & Electronics Engineering Energy Engineering Law, Crime, Criminology & Criminal Justice Materials Science & Nanotechnology Mathematics Public Health Social Sciences

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Journal : Contemporary Mathematics and Applications (ConMathA)

 1 
Analisis Kestabilan Model Matematika Penyebaran Penyakit Schistosomiasis dengan Saturated Incidence Rate Elda Widya; Miswanto Miswanto; Cicik Alfiniyah
Contemporary Mathematics and Applications (ConMathA) Vol. 2 No. 2 (2020)
Publisher : Universitas Airlangga

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20473/conmatha.v2i2.23851

Abstract

Schistosomiasis is a disease caused by infections of the genus Schistosoma. Schistosomiasis can be transmitted through schistosoma worms that contact human skin. Schistosomiasis is a disease that continues to increase in spread. Saturated incidence rates pay attention to the ability to infect a disease that is limited by an increase in the infected population. This thesis formulates and analyzes a mathematical model of the distribution of schistosomiasis with a saturated incidence rate. Based on the analysis of the model, two equilibrium points are obtained, namely non-endemic equilibrium points (E0) and endemic equilibrium points (E1). Both equilibrium points are conditional asymptotically stable. The nonendemic equilibrium point will be asymptotically stable if rh > dh, rs > ds and R0 < 1, while the endemic equilibrium point will be asymptotically stable if R0 > 1. Sensitivity analysis shows that there are parameters that affect the spread of the disease. Based on numerical simulation results show that when R0 < 1, the number of infected human populations (Hi), the number of infected snail populations (Si), the amount of cercaria density (C) and the amount of miracidia density (M) will tend to decrease until finally extinct. Otherwise at the time R0 > 1, the number of the four populations tends to increase before finally being in a constant state.
Analisis Kestabilan Model Matematika Predator-Prey pada Dinamika Sosial Laurensia Regina Bestari Gepak; Miswanto Miswanto; Cicik Alfiniyah
Contemporary Mathematics and Applications (ConMathA) Vol. 4 No. 1 (2022)
Publisher : Universitas Airlangga

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20473/conmatha.v4i1.34147

Abstract

In social life, difference and diversity is something that cannot be denied by anyone. Starting from differences horizontally concerning ethnicity, language, customs to religion and vertically concerning the political, social, cultural to economic fields. The existence of these many differences can certainly bring positive and negative impacts in social life. With diversity, interaction in society is dynamic, but it results in the emergence of negative attitudes such as egoism and competition between groups. From the occurrence of this can trigger the problem of social inequality in the community. Social inequality can occur because of national development efforts that only focus on economic aspects and forget about social aspects. The purpose of this thesis is to discuss the stability analysis of the predator-prey mathematical model on social dynamics with the Holling type II functional response. From this model analysis, we obtained four equilibrium points, which are the equilibrium point for the extinction of all population (E0) which is unstable, then the equilibrium point for the extinction of the non-poor population and the poor (E1) and the extinction of the non-poor population (E2) which are stable with certain conditions and coexistence (E3) which is to be asymptotically stable. Also in the final section, we perform the numerical simulation to supports the analytical result.
Analisis Kestabilan dan Kontrol Optimum pada Model Penyebaran Penyakit Influenza dengan Adanya Populasi Cross-Immune Bertha Aurellia Pamudya Fajar; Miswanto; Windarto
Contemporary Mathematics and Applications (ConMathA) Vol. 4 No. 2 (2022)
Publisher : Universitas Airlangga

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20473/conmatha.v4i2.39168

Abstract

Influenza is a respiratory tract infection known as flu. Caused by an RNA virus from Orthomyxoviridae family. This thesis aims to analyze the stability of the equilibrium point in the mathematical model of influenza transmission with Cross-Immune population and applying optimal control variables in the form of prevention and treatment. In this mathematical model of influenza transmission with Cross-Immune population, we obtain two equilibriums namely, the non- endemic equilibrium and the endemic equilibrium. Local stability and the existence of endemic equilibrium depend on the basic reproduction number (R0). The spread of influenza does not occur in the population when R0 < 1 and the spread of influenza persist in the population when R0 > 1. Furthermore, the problem of control variables in the mathematical model of influenza transmission is determined through the Pontryagin Maximum Principle method. The numerical simulation results show that treatment efforts are more effective in suppressing the spread of influenza disease than prevention efforts. However, giving control variables in the form of prevention and treatment at the same time is very effective in minimizing the number of human populations expose to and infected with influenza.
Analisis Kestabilan dan Kontrol Optimal Model Matematika Penyebaran Leptospirosis dengan Saturated Incidence Rate Miswanto; Nisrina Firsta Ammara; Windarto
Contemporary Mathematics and Applications (ConMathA) Vol. 5 No. 2 (2023)
Publisher : Universitas Airlangga

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20473/conmatha.v5i2.49379

Abstract

Leptospirosis is a disease caused by the bacteria Leptospira inchterohemorrhagiaea. Leptospirosis can attack humans and other animals, through rodents, especially rats. This research aims to analyze the stability of the equilibrium point in the mathematical model of the spread of Leptospirosis and apply optimal control variables in the form of prevention and treatment efforts. Based on the results of the mathematical model analysis of the spread of Leptospirosis, two equilibrium points were obtained, there are the non-endemic equilibrium point and the endemic equilibrium point. Local stability and the existence of an equilibrium point depend on the basic reproduction number ????0. The non-endemic equilibrium point is local asymptotically stable if ????0 < 1, while the endemic equilibrium point tends to be asymptotically stable if ????0 > 1. Next, the problem of control variables in the model is determined using Pontryagin's Maximum Principle. Numerical simulation results show that providing control in the form of prevention efforts and treatment efforts simultaneously provides effective results in minimizing the population of individuals exposed to and infected by Leptospirosis at the cost of providing optimal control.
Co-Authors Alfiniyah, Cicik Bertha Aurellia Pamudya Fajar Biba, Farah D. Mahayana Elda Widya Er Ayu Nurafifah Fatmawati Fatmawati H Muhammad H. Muhammad Mhammad I. Pranoto I. Pranoto Khusnul Khotimah, Bain Laurensia Regina Bestari Gepak Mahayana, D Millah, Nashrul Mohammad Imam Utoyo Nisrina Firsta Ammara Nunik Suroiyah Puja Nur Audria Sentot Achmadi Windarto Windarto Windarto Windarto, Windarto Yeni Kustiyahningsih